Chapter 12.7, Problem 27STP

To determine

To find:The lateral and surface area of the cone.

Answer to Problem 27STP

The lateral area of the cone is $282.6{\text{ cm}}^{\text{2}}$

The surface area of the cone is $395.64{\text{ cm}}^{\text{2}}$ .

Explanation of Solution

Given:

Radius of cone = 6 centimeters

Slant height = 15 centimeters.

Formula used:

The lateral area L of a cone is $L=\pi rl$ .

The surface area S of a cone is S=L+B.

Calculation:

Consider the cone whose radius is 6 cm and slant height is 15 cm.

Find the lateral area of the cone as follows:

Substitute $r=6\text{ and }l=15\text{ in }L=\pi rl.$

  $\begin{array}{l}L=\pi rl\\ \approx \pi (6)(15)\\ =90\pi \\ \approx 90(3.14)\text{ As }\pi \text{=3}\text{.14}\\ =282.6\end{array}$

Hence, the lateral area of the cone is approximately $282.6{\text{ cm}}^{\text{2}}$ .

Find the surface area of the cone as follows:

The area B of the basis is $B=\pi r^2$ .

  $\begin{array}{l}B=\pi r^2\\ $ =\pi {(6)}^2$=36\pi \\ \approx 36(3.14)\text{ As }\pi \text{=3}\text{.14}\\ =113.04\end{array}$

Substitute $B\approx 113.04\text{ and }L=282.6\text{ in }S=L+B$

  $\begin{array}{l}S=L+B\\ \approx 282.6+113.04\\ \approx 395.64\end{array}$

Conclusion:Hence, the lateral area of the cone is $282.6{\text{ cm}}^{\text{2}}$ &the surface area of the cone is $395.64{\text{ cm}}^{\text{2}}$ .